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The mapping properties of the radiosity operator along an edge
Author(s) -
Hansen Olaf
Publication year - 2002
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.329
Subject(s) - radiosity (computer graphics) , mathematics , sobolev space , operator (biology) , invertible matrix , enhanced data rates for gsm evolution , mathematical analysis , geometry , pure mathematics , computer graphics (images) , computer science , computer vision , biochemistry , chemistry , repressor , transcription factor , gene
In this article we study the radiosity operator along an edge between two adjacent half‐planes. First we show that the radiosity operator is invertible in a whole scale of anisotropic Sobolev spaces. In the absence of any shadows we are able to derive regularity properties of the solution, which depend only on the angle between the half‐planes, the reflectivity coefficients and the right‐hand side. This work can be considered as a supplement to the article of Rathsfeld ( Mathematical Methods in the Applied Sciences 1999; 22 : 217–241). Copyright © 2002 John Wiley & Sons, Ltd.